# 7.6 Entropy Change in Irreversible Processes - PowerPoint PPT Presentation

1 / 15

7.6 Entropy Change in Irreversible Processes.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

7.6 Entropy Change in Irreversible Processes

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### 7.6 Entropy Change in Irreversible Processes

• It is not possible to calculate the entropy change ΔS = SB - SA for an irreversible process between A and B, by integrating dq / T, the ratio of the heat increment over the temperature, along the actual irreversible path A-B characterizing the process.

• However, since the entropy is a state function, the entropy change ΔS does not depend on the path chosen.The calculation of an irreversible process can be carried out via transferring the process into many reversible ones:

• Three examples will be discussed here: (1) heat exchange between two metal blocks with different temperatures; (2) Water cooling from 90 to a room temperature; (2) A falling object.

## Thermodynamics Potential

Chapter 8

### 8.1 Introduction

• Thermodynamic potentials: Helmholtz function F and the Gibbs function G.

• The enthalpy, Helmholtz function and Gibbs functions are all related to the internal energy and can be derived with a procedure known as Legendre differential transformation.

• The combined first and second laws read

dU = Tds – PdV

where T and S, and -P and V are said to be canonically conjugate pairs.

• By assuming U = U(S,V), one has

### 8.2 The Legendre Transformation

• Consider a function Z = Z(x, y), the differential equation is dZ = Xdx + Ydy

where X and x, Y and y are by definition canonically conjugate pairs.

• We wish to replace (x, y) by (X, Y) as independent variables. This can be achieved via transforming the function Z(x,y) into a function M(X,Y).

• Assume M(X,Y) = Z(x,y) – xX – yY

Then dM = dZ – Xdx – xdX –Ydy – ydY

dM = -xdX - ydY

### 8.5 The Helmholtz Function

• The change in internal energy is the heat flow in an isochoric reversible process.

• The change in enthalpy H is the heat flow in an isobaric reversible process.

• The change in the Helmholtz function in an isothermal reversible process is the work done on or by the system.

• The decrease in F equals the maximum energy that can be made available for work.

### 8.6 The Gibbs Function

• Based on the second law of thermodynamics

dQ ≤ T∆S with dQ = ∆U + P ∆V

• Combine the above expressions

∆U + P ∆V ≤ T∆S

∆U + P ∆V - T∆S ≤ 0

• Since G = U + PV –TS

(∆G)T,P≤ 0 at constant T and P

or G f ≤ Gi

• Gibbs function decreases in a process until a minimum is reach, i.e. equilibrium point.

• Note that T and P need not to be constant throughout the process, they only need to have the same initial and final values.